Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations

被引：43
|
作者：
Imbert, Cyril [1 ]
机构：
[1] Univ Paris 09, CEREMADE, CNRS, UMR 7534, F-75775 Paris 16, France
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 250卷 / 03期
关键词：
Degenerate fully non-linear elliptic equation; Singular fully non-linear elliptic equation; Non-divergence form; Alexandroff-Bakelman-Pucci estimate; Weak Harnack inequality; Local maximum principle; Harnack inequality; Holder regularity; Viscosity solutions; PARTIAL-DIFFERENTIAL EQUATIONS; VISCOSITY SOLUTIONS; MAXIMUM PRINCIPLE; LINEAR EQUATIONS;
D O I：
10.1016/j.jde.2010.07.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate or singular when "the gradient is small". Typical examples are either equations involving the m-Laplace operator or Bellman-lsaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such non-linear elliptic equations. (C) 2010 Elsevier Inc. All rights reserved.
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页码：1553 / 1574
页数：22
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